Correlating residuals in BSEM?
Message/Author
 Fredrik Falkenström posted on Monday, December 16, 2013 - 9:51 am
Dear Drs Muthén,

I am using BSEM with zero mean, small variance priors for correlating residuals in a longitudinal measurement invariance analysis. I noticed that I can either estimate residuals for each measurement occasion while ignoring residuals across time (i.e. constraining these to zero), or I can estimate all possible residuals. However, when I tried to estimate all residuals within each time-point + only residuals for the same items across time while constraining all other residuals across time to zero, I got the following error message:

*** FATAL ERROR
THE VARIANCE COVARIANCE MATRIX IS NOT SUPPORTED. ONLY FULL VARIANCE COVARIANCE BLOCKS ARE ALLOWED. USE ALGORITHM=GIBBS(RW) TO RESOLVE THIS PROBLEM.

What is the reason for this? I can understand if I had to estimate all possible correlations or none at all, but it seems fine to estimate only the ones from the same measurement occasion. Can Mplus really know that the variables from the same occasion are related?

Best regards,

Fredrik Falkenström
 Bengt O. Muthen posted on Monday, December 16, 2013 - 11:00 am
The current default Bayes algorithm supports covariance matrix structures with uncorrelated blocks of correlated variables like the two uncorrelated blocks

x
x x
0 0 x
0 0 x x

but not for instance

x
x x
0 0 x
x 0 x x

The error message stops a structure like the second one when using the default algorithm.
 Fredrik Falkenström posted on Tuesday, December 17, 2013 - 2:25 am
Ok, thanks for explaining. Can you recommend a good reference for reading about the Gibbs(RW) algorithm? I get other error messages when I try to switch to Gibbs(RW), so I guess I need to know more about this.

Best,

Fredrik
 Fredrik Falkenström posted on Tuesday, December 17, 2013 - 4:58 am
I noticed after experimenting a bit that Gibbs(RW) works if I specify priors as normally distributed rather than Inverse Wishart. Could you explain how to specify priors using the Gibbs(RW) algorithm?

Best,

Fredrik
 Tihomir Asparouhov posted on Tuesday, December 17, 2013 - 3:53 pm
Here are the references for the methodology

section 3.3.4 in

Gibbs(RW) accepts only univariate priors so IW is not allowed. Priors are specified the same way as for other algorithms

model: y1 with y2 (a);
model prior: a~N(0, 0.3);